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Solution to Exercise 3

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motion: TOC for Knowledge Concepts, Exercises, and Solutions

(a) Hmm.  I trim my fingernails about once a month, and they've grown out about an 
eighth of an inch each time, so my fingernails grow at

 (1/8 inch/mo) * (12 mo/yr) = 1.5 inches per year.

(b) Hmm.  I get my hair cut about once a month, and my hair has grown out about an 
inch each time, so my hair grows at about

 (1 inch/mo) * (12 mo/yr) = 12 inches per year.

(c) Since I've estimated in all my calculations (including for Exercise 2 above) 
using "numerical sense," an answer that's twice as
big or twice as small as another answer can be considered approximately the same.  
Since I calculated above that the continents are moving about 3 inches per year, I 
feel confident enough to assert that my fingernails grow at roughly the same speed 
as the continents drift!  My hair apparently grows faster, though - 12 inches per 
year is a somewhat larger value than 3 inches per year. 

Again, the key words are "about," "approximately," and "roughly."  If you 
challenged my assertion that my hair grows faster than the continents drift, I 
wouldn't be insulted in the least; you need only convince me that one or more of 
my estimates didn't make numerical sense.  Perhaps you may assert that my hair 
grows only a quarter inch a month.  Then, I might reply that if my hair grew only 
a quarter inch, I wouldn't bother to get it cut.  So the numerical sense debates 
move forward - and we learn something about our universe in the meantime!